Continuous stirred tank reactor material balance

Fig. 1.17. Continuous stirred-tank reactor material balance over rth tank in steady state...

Continuous. stirred tank reactor (CSTR), with the effluent concentration the same as the uniform vessel concentration. With a mean residence time t = V /V, the material balance is... 

The ideal continuous stirred tank reactor is the easiest type of continuous flow reactor to analyze in design calculations because the temperature and composition of the reactor contents are homogeneous throughout the reactor volume. Consequently, material and energy balances can be written over the entire reactor and the outlet composition and temperature can be taken as representative of the reactor contents. In general the temperatures of the feed and effluent streams will not be equal, and it will be necessary to use both material and energy balances and the temperature-dependent form of the reaction rate expression to determine the conditions at which the reactor operates. 

Continuous Stirred Tank Reactor (CSTR). The conversion degree of the azo-dye, the reaction volume (V) and the volumetric flow rate (Q) of the dye-bearing stream are related to each other through the material balance referred to the dye and extended to the reactor volume. Assuming an unstructured model for the biophase, the material balance yields... 

Data obtained in continuous stirred tank reactors have the merits of isothermicity and of an algebraic relation between the variables rather than a differential one. At steady state In a CSTR the material balance on a reactant A is... 

A continuous stirred tank reactor battery ICSTR) Material balances ... 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

Continuous Stirred-Tank Reactor — One Tank Taking material balances in the steady state as shown in Fig. 1.26 ... 

The semibatch reactor is a cross between an ordinary batch reactor and a continuous-stirred tank reactor. The reactor has continuous input of reactant through the course of the batch run with no output stream. Another possibility for semibatch operation is continuous withdrawal of product with no addition of reactant. Due to the crossover between the other ideal reactor types, the semibatch uses all of the terms in the general energy and material balances. This results in more complex mathematical expressions. Since the single continuous stream may be either an input or an output, the form of the equations depends upon the particular mode of operation. 

Reactor Tracer Responses Continuous Stirred Tank Reactor (CSTR) With magnitude Cf, the unsteady material balance of tracer a step input of... 

In an ideal continuous stirred tank reactor, composition and temperature are uniform throughout just as in the ideal batch reactor. But this reactor also has a continuous feed of reactants and a continuous withdrawal of products and unconverted reactants, and the effluent composition and temperature are the same as those in the tank (Fig. 7-fb). A CSTR can be operated under transient conditions (due to variation in feed composition, temperature, cooling rate, etc., with time), or it can be operated under steady-state conditions. In this section we limit the discussion to isothermal conditions. This eliminates the need to consider energy balance equations, and due to the uniform composition the component material balances are simple ordinary differential equations with time as the independent variable ... 

Consider a continuously stirred tank reactor (CSTRs) sustaining the series reaction (A—-—>B —-—>C ).[1], [9] The material balance equations are as follows ... 

A mixed-flow reactor (MFR), also known as the continuous stirred tank reactor (CSTR), is fuUy mixed at the molecular level, and the composition of the exiting stream is identical to that within the reactor. In this case, the material balance of Equation (11.12) is applied for the entire reactor and not just for a differential element as in a PFR. No integration is needed the eqnation becomes... 

Reactions orders and rate coefficients can be established with methods that use either rate or concentration data. Batch, tubular plug-flow, and differential recycle reactors yield concentrations as directly measured quantities, and calculation of rates requires finite-difference approximations. To avoid these, concentration methods should be used. In contrast, continuous stirred-tank reactors allow rates to be calculated from material balances without approximation. Here, evaluation based on rates is equally suited. 

In writing the material balance equations for a compartment, several assumptions are made. The transport terms between each of the subcompartments are defined, the binding of drug in each subcompartment is quantified and incorporated into the equations, and additional terms are included where necessary to account for liver clearance, kidney clearance, and intestinal absorption. Each subcompartment, i.e., the vascular, the interstitial, and the intracellular, is considered to be a perfectly mixed continuous-stirred-tank reactor (CSTR). This means the concentration of each subcompartment has no spatial dependence. 

As the main responsible for the changes in the material balance, the chemical reactor must be modelled accurately from this point of view. Basic flowsheeting reactors are the plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), as shown in Fig. 3.17. The ideal models are not sufficient to describe the complexity of industrial reactors. A practical alternative is the combination of ideal flow models with stoichiometric reactors, or with some user programming. In this way the flow reactors can take into account the influence of recycles on conversion, while the stoichiometric types can serve to describe realistically selectivity effects, namely the formation of impurities, important for separations. Some standard models are described below. 

A continuously stirred tank reactor (CSTR) battery Material balances n aO = K + ralVrl... 

The performance equation for a continuous stirred tank reactor (CSTR) was developed in Chapter 4. We use the same equation now but with a complex rate equation replacing the simpler one of the earlier chapter. We describe the method for any complex reaction consisting of N components and M reactions. The following material balances can be written for the different constituents of the complex reaction at hand (see Figure 11.2) ... 

Stoichiometry - Conversions Using Balanced Equations http //www.youtube.com/watch v=wySZDEbqbnM Two Continuous Stirred Tank Reactors in Series http //www.youtube.com/watch v=7RLQ9sHkdkk Balances on Multiple Units with Reaction https //www.youtube.com/watch v=tQyrSvll nc Extent of Reaction for Material Balances https //www.youtube.com/watch v=YusSUOjlOUk Three Methods for Solving Reactive Material Balances https //www.youtube.com/watch v=MSzTIRAv5io... 

A similar approach, starting with a material balance, can be used for the characterization of bioreactors operating in the continuous mode. Thus, for a perfectly mixed reactor, or continuous stirred tank reactor (CSTR), where the term of accumulation is zero at steady state and the liquid composition is uniform, the material balance for substrate A is given by Equation 7.7 ... 

The contents of a continuous stirred tank reactor (CSTR) are well mixed and are taken to be of a uniform concentration. Thus there is no need to take balances on differential volumes. The material balance equation for the reactor shown in figure 7.5 is simply... 

It is desired to determine the steady-state temperature and concentration in a continuous stirred tank reactor in which an exothermic reaction is taking place. We want to determine conditions for both maximum and minimum cooling. The reactor is shown in Figme 2.22. The macroscopic material and energy balances are... 

As shown in Chapter 2, a continuous stirred-tank reactor with a single first-order chemical reaction has the following material and energy balances ... 

Solves a set of simultaneous linear algebraic equations that represent the material balances for a set of continuous stirred tank reactors using the Jacobi Iterative method (Jacobi.m). 

Consider the schematic representation of a continuous flow stirred tank reactor shown in Figure 8.5. The starting point for the development of the fundamental design equation is again a generalized material balance on a reactant species. For the steady-state case the accumulation term in equation 8.0.1 is zero. Furthermore, since conditions are uniform throughout the reactor volume, the material balance may be... 

The material balance for a continuous-flow, stirred-tank reactor with constant volume and first-order reaction is... 

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